A string of natural length L extends to a new length L' under tensile force F. If Hooke’s law applies, the work done in stretching the spring is _________________
The work done in stretching the spring can be calculated using the formula for work, which is given by:
Work = Force x Displacement
In the case of Hooke's law, the force is directly proportional to the displacement or extension of the spring. Therefore, we can write the force as:
F = kΔL
where k is the spring constant and ΔL is the change in length.
Given that the natural length of the spring is L and it extends to a new length L', the change in length is:
ΔL = L' - L
Substituting this into the equation for force, we get:
F = k(L' - L)
Finally, we can calculate the work done by multiplying the force by the displacement:
Work = F x ΔL
Work = k(L' - L) x ΔL
Therefore, the work done in stretching the spring is k(L' - L) multiplied by the change in length, ΔL.